Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

Hydraulic Turbines 315
gave measured values of the maximum efficiencies of 0.85 and 0.90 for the model and
full-scale turbines, respectively, which agreed very well with the ratio computed with
n = 0.25 in the Moody formula!
Example 9.5. A model of a Francis turbine is built to a scale of 1/5 of full size and
when tested it developed a power output of 3kW under a head of 1.8m of water, at a
rotational speed of 360rev/min and a flow rate of 0.215m 3 /s. Estimate the speed, flow
rate and power of the full-scale turbine when working under dynamically similar conditions
with a head of 60m of water.
By making a suitable correction for scale effects, determine the efficiency and the
power of the full-size turbine. Use Moody’s formula and assume n = 0.25.
Solution. From the group y = gH/(ND) 2 we get
From the group f = Q/(ND 3 ) we get
Lastly, from the group Pˆ = P/(rN 3 D 5 ) we get
This result has still to be corrected to allow for scale effects. First we must calculate
the efficiency of the model turbine. The efficiency is found from
Using Moody’s formula the efficiency of the prototype is determined:
hence
The corresponding power is found by an adjustment of the original power obtained
under dynamically similar conditions, i.e.
Cavitation
A description of the phenomenon of cavitation, mainly with regard to pumps, was
given in Chapter 1. In hydraulic turbines, where reliability, long life and efficiency are
all so very important, the effects of cavitation must be considered. Two types of cavitation
may be in evidence,
(i) on the suction surfaces of the runner blades at outlet which can cause severe blade
erosion; and
(ii) a twisting “rope-type” cavity that appears in the draft tube at off-design operating
conditions.